Process for producing purified silicon

ABSTRACT

Provided is a process for producing a purified silicon by cutting off a crude silicon region, without determining the aluminium concentration in a directionally-solidified silicon. 
     In the process of the invention, a standard solidification fraction (f 0 ) satisfying the following formula (1) and formula (2) is obtained from the predetermined maximum level of aluminium concentration (C 10max ), the temperature gradient (T) and the solidification speed (R), and the directionally-solidified silicon is cut at the part having a solidification fraction (f) in the solidification step corresponding to f 0 . 
     
       
         
           
             
               
                 
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     [wherein k is a coefficient selected from a range of from 0.9 times to 1.1 times the effective aluminium partitioning coefficient k′, as obtained so as to satisfy the following formula (2): 
         C   10max   =k′×C   2 ×(1− f   0 ) k′−1    (2), 
     (k′ is an effective aluminium partitioning coefficient, C 2  is the aluminium concentration of the starting silicon material melt)].

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a process for producing purified silicon, precisely to a process for producing purified silicon according to a directional solidification process that comprises cooling and solidifying an aluminium-containing, starting silicon material melt in a mold under a unidirectional temperature gradient condition to give a solidified substance (hereinafter referred to as “directionally-solidified silicon”).

2. Description of the Related Art

As a process for producing purified silicon (1) by removing aluminium from an aluminium-containing starting silicon material melt (2), a directional solidification process that comprises cooling and solidifying a starting silicon material melt (2) in a mold (3) under a unidirectional temperature gradient (T) condition is known, as in FIG. 1 and FIG. 2. According to the process, the starting silicon material melt (2) is solidified under aluminium segregation of such that aluminium precipitation on the low-temperature side (21) under the temperature gradient (T) is small. Then, aluminium is thickened in the direction toward the high-temperature side (22), thereby giving a directionally-solidified silicon (4). The directionally-solidified silicon (4) is divided into two region including a purified silicon region (41) existing on the low-temperature side (21) under the temperature gradient (T) in solidification and having a relatively low aluminium concentration (C), and a crude silicon region (45) existing on the high-temperature side (22) under the temperature gradient (T) and having a relatively high aluminium concentration (C) (FIG. 2). The purified silicon region (41) having a relatively low aluminium concentration (C) is separated by cutting off the crude silicon region (45) from the directionally-solidified silicon (4), accordingly the intended purified silicon (1) is obtainable (JP-A 2004-196577).

In case where the predetermined maximum level of aluminium concentration (C_(10max)) in the purified silicon (1) is set high, a part of the purified silicon (1) corresponding to relatively high solidification fraction (f) is included in the purified silicon region (41). The solidification fraction (f) increases with the progress of solidification of the starting silicon material melt (2) according to the directional solidification process as shown in FIG. 2. Accordingly, at the part having a high solidification fraction (f), the directionally-solidified silicon (4) may be cut to give the intended purified silicon (1). On the contrary, in case where the allowable aluminium limit is set low, the directionally-solidified silicon (4) may be cut at the part having a small solidification fraction (f), thereby giving the intended purified silicon (1).

Heretofore the relationship between the temperature gradient (T), the solidification speed (R), the aluminium concentration (C), and the solidification fraction (f) in the obtained directionally-solidified silicon (4) was not clear. In case where a starting silicon material melt is solidified under untried temperature gradient (T) and untried solidification speed (R) conditions, the aluminium concentration (C) is actually measured over the whole of the obtained directionally-solidified silicon (4) to identify the part at which the concentration (C) is the predetermined maximum level of aluminium concentration (C_(10max)), and the directionally-solidified silicon (4) is cut at this part.

Given that situation, the present inventors have assiduously studied to develop a process capable of producing the intended purified silicon (1) by cutting off the crude silicon region (45) without actual measurement of the aluminium concentration (C) over the whole of the directionally-solidified silicon (4), and as a result, have reached the present invention.

SUMMARY OF THE INVENTION

Specifically, the invention provides a process for producing a purified silicon (1) by using a silicon melt (2) as a starting material, comprising:

a step of solidifying an aluminium-containing starting silicon material melt (2) by cooling in a mold (3) under a unidirectional temperature gradient (T (° C./mm)) condition to give a directionally-solidified silicon (4) containing a purified silicon region (41) having an aluminium concentration (C (ppm)) not higher than the predetermined maximum level of aluminium concentration (C_(10max) (ppm)) and a crude silicon region (45) having an aluminium concentration (C) higher than the predetermined maximum level of aluminium concentration (C_(10max)), and a step of cutting off the crude silicon region (45) from the obtained directionally-solidified silicon (4) to give a purified silicon (1) having an aluminium concentration (C) not higher than the predetermined maximum level of aluminium concentration (C_(10max)),

wherein, in the step of cutting off the crude silicon region (45), the directionally-solidified silicon (4) is cut at a part corresponding to a standard solidification fraction (f₀) obtained from the predetermined maximum level of aluminium concentration (C_(10max)) and the temperature gradient (T) and the solidification speed (R (mm/min)) in cooling the starting silicon material melt (2) and satisfying the following formula (1) and formula (2), thereby cutting off the crude silicon region (45); the standard solidification fraction (f₀) indicates the ratio of the purified silicon region (41) having an aluminium concentration (C (ppm)) not higher than the predetermined maximum level of aluminium concentration (C_(10max) (ppm)), to the whole of the directionally-solidified silicon (4), and 0≦f₀≦1;

$\begin{matrix} {k = {{\left\{ {{K_{1} \times {{Ln}(R)}} + K_{2}} \right\} \times \left\{ {K_{3} \times {\exp \left\lbrack {K_{4} \times R \times \left( {{K_{5} \times C_{2}} + K_{6}} \right)} \right\rbrack}} \right\} \times \left\{ {{K_{7} \times T} + K_{8}} \right\}} - K_{9}}} & (1) \end{matrix}$

[in formula (1), k is a coefficient selected from a range of from 0.9 times to 1.1 times the effective aluminium partitioning coefficient k′, as obtained so as to satisfy the following formula (2):

C _(10max) =k′×C ₂×(1−f ₀)^(k′−1)   (2),

-   K₁ means a constant selected from a range of 1.1×10⁻³±0.1×10⁻³, -   K₂ means a constant selected from a range of 4.2×10⁻³±0.1×10⁻³, -   K₃ means a constant selected from a range of 1.2±0.1, -   K₄ means a constant selected from a range of 2.2±0.1, -   K₅ means a constant selected from a range of −1.0×10⁻³±0.1×10⁻³, -   K₆ means a constant selected from a range of 1.0±0.1, -   K₇ means a constant selected from a range of −0.4±0.1, -   K₈ means a constant selected from a range of 1.36±0.01, -   K₉ means a constant selected from a range of 2.0×10⁻⁴±1.0×10⁻⁴, -   R means a solidification speed (mm/min), -   T means a temperature gradient (° C./mm)],     [in formula (2), C_(10max) means the predetermined maximum level of     aluminium concentration (ppm) in purified silicon, C₂ means the     aluminium concentration(ppm) in the starting silicon material melt,     and f₀ means the standard solidification fraction].

According to the production process of the invention, based on the standard solidification fraction (f₀) obtained from the predetermined maximum level of aluminium concentration (C_(10max)) and the temperature gradient (T) and the solidification speed (R) in the step of solidifying the starting silicon material melt (2), the directionally-solidified silicon (4) is cut, and therefore, the purified silicon (1) having an aluminium concentration (C) not higher than the predetermined maximum level of aluminium concentration (C_(10max)) can be produced without actually measuring the aluminium concentration (C) in the directionally-solidified silicon (4).

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a cross-sectional view schematically showing a process of obtaining a directionally-solidified silicon from a starting silicon material melt according to a directional solidification process.

FIG. 2 is a cross-sectional view schematically showing a process of obtaining a purified silicon from a directionally-solidified silicon.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The process of the invention is described below with reference to FIG. 1 and FIG. 2. The reference numerals used in FIG. 1 and FIG. 2 are described as follows: The reference numeral 1 is a purified silicon; 2 is a starting silicon material melt; 21 is a low-temperature side of temperature gradient, 22 is a high-temperature side of temperature gradient; 24 is a solid phase; 25 is a liquid phase; 26 is an interface; 3 is a mold; 4 is a directionally-solidified silicon; 41 is a purified silicon region; 45 is a crude silicon region; 5 is a crude silicon; 6 is a heater; 7 is a furnace; 8 is a water-cooling plate. In the following description, the reference sign T means a temperature gradient; and f₀ means a standard solidification fraction.

The starting silicon material melt (2) for use in the process of the invention is silicon melted by heating, and its temperature is over the melting point (about 1414° C.) of silicon and is generally from 1420° C. to 1580° C.

The starting silicon material melt (2) contains aluminium. The aluminium concentration (C₂) in the starting silicon material melt (2) is generally from 10 ppm to 1000 ppm, preferably at most 15 ppm. When the aluminium concentration (C₂) in the starting silicon material melt is less than 10 ppm, it may be difficult to further remove aluminium from the melt; but when the concentration is over 1000 ppm, then an excess temperature gradient (T) and solidification fraction (R) may be necessary for obtaining the purified silicon (1), but such is impracticable.

In addition to aluminium, the starting silicon material melt (2) may contain any other impurity elements than silicon and aluminium so far as their amount is small, concretely, at most 1 ppm in total; but in particular, the content of boron and phosphorus in the melt is preferably as small as possible, concretely, at most 0.3 ppm each, more preferably at most 0.1 ppm each.

In the process of the invention, the starting silicon material melt (2) is cooled in a mold (3), like in an ordinary directional solidification process. As the mold (3), generally used is one inert to the starting silicon material melt (2) and resistant to heat. Concretely used is one formed of carbon such as graphite, or silicon carbide, nitrogen carbide, alumina (aluminium oxide), silica (silicon oxide) such as quartz or the like.

The cooling is attained under a unidirectional temperature gradient (T) condition of the starting silicon material melt (2). The temperature gradient (T) may be provided unidirectionally, for example, in a horizontal direction so that the low-temperature side (21) and the high-temperature side (22) may be on the same height, or in a gravity direction so that the low-temperature side (21) may be in the upper part and the high-temperature side (22) may be in the lower part. In general, the low-temperature side (21) is in the lower part and the high-temperature side (22) is in the upper part, thereby giving a temperature gradient (T) in the gravity direction, as in FIG. 1. The temperature gradient (T) may be generally from 0.2° C./mm to 1.5° C./mm, preferably from 0.4° C./mm to 0.9° C./mm, more preferably from at least 0.7° C./mm, because any excess equipment is not required and practicable not requiring any excess equipment, and it is practicable.

The temperature gradient (T) may be generated, for example, according to a process of heating the upper part of the mold (3) with the heater (6) in a furnace (7) equipped with a heater (6) and opened to air at the lower side thereof with cooling the lower part of the mold below the furnace (7). For cooling the lower part of the mold (3), the lower part may be left cooled in air; or depending on the temperature gradient (T), for example, a water-cooling plate (8) may be provided below the furnace (7) and the lower part of the mold (3) may be cooled by the water-cooling plate (8).

The starting silicon material melt (2) may be cooled from the bottom, for example, by moving the mold (3) containing the melt therein, in the lower direction, and leading the mold outside the furnace (7) from the bottom thereof. The starting silicon material melt (2) is cooled from the bottom in that manner, whereby the starting silicon material melt (2) begins to solidify from the low-temperature side (21) with forming a solid phase (24), thereby giving a directionally-solidified silicon (4).

The solidification speed (R) is represented by the moving speed of the interface (26) between the solid phase (24) formed from the low-temperature side (21) by cooling, and the liquid phase (25) not as yet solidified on the high-temperature side (22); and the solidification speed (R) may be controlled by the moving speed of the mold (3) while the mold (3) is moved outside the furnace (7). The solidification speed (R) may be generally from 0.05 mm/min to 2 mm/min, preferably from 0.1 mm/min to 1 mm/min.

In the process of solidifying the starting silicon material melt (2) by cooling in the manner as above, aluminium contained in the starting silicon material melt (2) segregates on the high-temperature side (22). Accordingly, after solidification, the aluminium content (C) in the directionally-solidified silicon (4) is one increasing unidirectionally from the low-temperature side (21) to the high-temperature side (22) under the temperature gradient (T). The region on the low-temperature side (21) under the temperature gradient (T) in the cooling process is the purified silicon region (41) having a lower aluminium content, and the region on the high-temperature side (22) is the crude silicon region (45) containing a large amount of segregated aluminium. The intended purified silicon (1) is produced by cutting off the crude silicon region (45) from the directionally-solidified silicon (4). The method of cutting off the crude silicon region (45) is not specifically defined. For example, the directionally-solidified silicon (4) may be cut according to an ordinary method of using a diamond cutter to thereby cut off the crude silicon region (45).

In the above-mentioned directional solidification process where the starting silicon material melt (2) solidified in one direction, where a solidification fraction (f) that increases along the solidification direction is set as an index indicating the progress of solidification, the standard solidification fraction (f₀) is computed according to a process mentioned below and the directionally-solidified silicon (4) is cut at the part where the solidification fraction (f) corresponds to the standard solidification fraction (f₀) to cut off the crude silicon region (45) in the process of the invention. The solidification fraction (f) at the solidification starting site is 0, and the solidification fraction (f) at the solidification ending site is 1.

In detail, the solidification fraction (f) indicates the ratio of the solid phase (24) solidified in the process of cooling and solidifying the starting silicon material melt (2), to the starting silicon material melt (2) used for the solidification. In the process of the invention, the directionally-solidified silicon (4) is obtained by cooling under a unidirectional temperature gradient (T) condition, and the solidification fraction (f) of the obtained directionally-solidified silicon (4) may increase along the direction of the temperature ingredient (T).

The standard solidification fraction (f₀) is determined so as to satisfy the above-mentioned formula (1). The coefficient k in formula (1) can be considered the same as the effective aluminium partitioning coefficient (k′) with allowing a difference of ±0.1 times therebetween, and hereinunder the coefficient k is also referred to as an effective aluminium partitioning coefficient. The effective aluminium partitioning coefficient (k′) that has close relation to the coefficient k is determined so as to satisfy the above-mentioned formula (2).

The formula (2) is derived from a formula (2-1) indicating the relationship between the solidification fraction (f) and the aluminium concentration (C) in the part having become the solid phase (23) just before the solidification (the part corresponding to the solidification fraction (f)):

C=k′×C ₂×(1−f)^(k′−1)   (2-1)

[wherein C means the aluminium concentration (ppm) in the solid phase, k′ means the effective aluminium partitioning coefficient, C₂ means the aluminium concentration (ppm) in the starting silicon material melt (2) used for the solidification, and f means the solidification fraction].

The formula (2-1) is a relational formula generally referred to as a Shair's formula (“Solidification of Metal” (published on Dec. 25, 1971 by Maruzen Publishing), pp 121-134).

The predetermined maximum level of aluminium concentration (C_(10max)) is generally from 1/1000 times to 3/100 times the aluminium concentration (C₂) in the starting silicon material melt (2).

The formula (1) indicates the relation between the effective aluminium partitioning coefficient (k), and the solidification speed (R) and the temperature gradient (T), and was established for the first time by the present inventors.

In the process of the invention, the directionally-solidified silicon (4) is cut after solidification, based on the standard solidification fraction (f₀) satisfying the formula (1).

In the directionally-solidified silicon (4) obtained by solidifying a starting silicon material melt (2) according to the process of the invention, the low-temperature side (21) under the temperature gradient (T) in the cooling step is a purified silicon region (41), and the high-temperature side (22) is a crude silicon region (45). In the part where the solidification fraction (f) in the solidification step corresponds to or is smaller than the standard solidification fraction (f₀), the aluminium concentration (C) is the same as or lower than the predetermined maximum level of aluminium concentration (C_(10max)), and in the part where the solidification fraction (f) is larger than the standard solidification fraction (f₀), the aluminium concentration (C) is larger than the predetermined maximum level of aluminium concentration (C_(10max)); and accordingly, the crude silicon region (45) can be removed by cutting the directionally-solidified silicon (4) is cut at the part having a solidification fraction (f) corresponding to the standard solidification fraction (f₀), whereby the intended purified silicon (1) having an aluminium concentration (C) lower than the predetermined maximum level of aluminium concentration (C_(10max)) can be obtained.

The obtained purified silicon (1) may be further purified according to a process of washing with acid or the like. The acid to be used for the acid washing may be generally a mineral acid such as hydrochloric acid, nitric acid or sulfuric acid, and from the viewpoint of preventing environmental pollution, generally used is one having few metal impurities. The obtained purified silicon (1) may be melted under heat, and may be used as the starting silicon material melt (2) in the process of the invention, whereby a purified silicon having a further reduced aluminium content can be obtained.

The removed crude silicon (5) may be melted under heat along with silicon having a smaller aluminium content than this, and may be again used as the starting silicon material melt (2) in the invention.

The purified silicon (1) obtained according to the process of the invention can be favorably used, for example, as a starting material for solar cells, etc.

EXAMPLES

The invention is described in more detail with reference to the following Examples, by which, however, the invention should not be limited.

Reference Example 1 Computation of Formula (1)

In computation in the following Examples, k=1.0×k′.

Experiment 1:

Using an apparatus of FIG. 1, a starting silicon material melt (2) having an aluminium concentration (C₂) of 1000 ppm was cooled in a mold (3) under a temperature gradient (T) (0.9° C./mm) condition so as to be solidified at a solidification speed (R) of 0.4 mm/min, thereby giving a directionally-solidified silicon (4). In the obtained directionally-solidified silicon (4), the aluminium concentration (C) in the part having a solidification fraction (f) in the cooling step of 0.18 and 0.38 was determined through ICP (inductively coupled plasma) emission spectrometry or ICP mass spectrometry, and was 4.0 ppm (f=0.18) and 4.9 ppm (f=3.08), respectively. From the solidification fraction (f) and the aluminium concentration (C), the effective aluminium partitioning coefficient (k) satisfying the formula (2-1) was obtained, and was 3.1×10⁻³. The results are shown in Table 1.

Experiment 2 and Experiment 3:

The starting silicon melt (2) having an aluminium concentration (C₂) shown in Table 1, in place of the starting silicon material melt (2) used in Experiment 1, was cooled under a temperature gradient (T) condition shown in Table 1 so as to be solidified at a solidification speed (R) shown in Table 1, and in the obtained directionally-solidified silicon (4), the aluminium concentration (C) in the part having a solidification fraction (f) in the cooling step as in Table 1 was determined, in the same manner as in Experiment 1, thereby determining the effective aluminium partitioning coefficient (k) in each case. The results are shown in Table 1.

TABLE 1 Experiment C₂ T R C No. ppm ° C./mm mm/min f ppm k 1 1000 0.9 0.4 0.18 4.0 3.1 × 10⁻³ 0.38 4.9 2 1000 0.9 0.2 0.17 2.8 2.5 × 10⁻³ 0.38 4.2 3 1000 0.9 0.05 0.32 1.2 0.8 × 10⁻³ 0.72 2.6

From the results in Experiment 1 to Experiment 3, the relation between the solidification speed (R) and the effective aluminium partitioning coefficient (k) was obtained, as indicated by the following formula (1-1):

k={K ₁ ×Ln(R)+K ₂′}  (1-1)

[wherein k means the effective aluminium partitioning coefficient; and R means the solidification speed (mm/min)].

In formula (1-1), K₁′ is 1.1×10⁻³, and K₂′ is 4.2×10⁻³.

In Experiment 1 to Experiment 3, the temperature gradient (T), the solidification speed (R) and the effective aluminium partitioning coefficient (k) satisfy the formula (1-1).

Experiment 4 to Experiment 6:

Experiment 4 to Experiment 6 are the same as the above-mentioned Experiment 1 to Experiment 3 in point of the temperature gradient (T), but differ from them in point of the aluminium concentration (C₂) in the starting silicon material melt (2). The aluminium concentration (C₂) in the starting silicon material melt (2), the temperature gradient (T), and the solidification speed (R) are shown in Table 2. In the obtained directionally-solidified silicon (4), the aluminium concentration (C) in the part having a solidification fraction (f) in the cooling step as in Table 2 was determined; and in the same manner as in Experiment 1, the effective aluminium partitioning coefficient (k) in each case was determined. The results are shown in Table 2.

TABLE 2 Experiment C₂ T R C No. ppm ° C./mm mm/min f ppm k 4 100 0.9 0.2 0.17 0.4 4.1 × 10⁻³ 0.45 1.1 5 10 0.9 0.4 0.32 0.1 9.0 × 10⁻³ 0.72 0.3 6 10 0.9 0.2 0.20 0.05 4.2 × 10⁻³ 0.52 0.17

These Experiment 4 to Experiment 6 are the same as Experiment 1 to Experiment 3 in point of the temperature gradient (T), but differ from them in point of the aluminium concentration (C₂) in the starting silicon material melt (2). The effective aluminium partitioning coefficient (k) obtained in these Experiment 4 to Experiment 6 does not satisfy the above-mentioned formula (1-1).

As a formula satisfying the effective aluminium partitioning coefficient (k) determined in the above-mentioned Experiment 1 to Experiment 3 and further satisfying the effective aluminium partitioning coefficient (k) determined in these Experiment 4 to Experiment 6, obtained was the following formula (1-2):

k={K ₁ ′×Ln(R)+K ₂ ′}×{K ₃′×exp[K ₄ ′×R×(K ₅ ′×C ₂ +K ₆′)]}  (1-2)

[wherein k, R, K₁′ and K₂′ have the same meanings as above; and C₂ means the aluminium concentration (ppm) in the starting silicon material melt].

In formula (1-2), K₃′ is 1.2, K₄′ is 2.2, K₅′ is −1.0×10⁻³, and K₆′ is 1.0.

The temperature gradient (T), the solidification speed (R), the aluminium concentration (C₂) in the starting silicon material melt (2) used and the effective aluminium partitioning coefficient (k) in Experiment 1 to Experiment 3 and Experiment 4 to Experiment 6 satisfy the formula (1-2).

Experiment 7:

Experiment 7 is the same as the above-mentioned Experiment 2 in point of the aluminium concentration (C₂) in the starting silicon material melt (2) but differs from the latter in the temperature gradient (T). The aluminium concentration (C₂) in the starting silicon material melt (2), the temperature gradient (T) and the solidification speed (R) are as in Table 3. In the obtained directionally-solidified silicon (4), the aluminium concentration (C) in the part having a solidification fraction (f) in the cooling step as in Table 3 was determined; and in the same manner as in Experiment 1, the effective aluminium partitioning coefficient (k) was determined. The results are shown in Table 3.

TABLE 3 Experiment C₂ T R C No. ppm ° C./mm mm/min f ppm k 7 1000 0.4 0.2 0.17 3.1 3.0 × 10⁻³ 0.52 6.7

This Experiment 7 is the same as Experiment 2 in point of the aluminium concentration (C₂) in the starting silicon material melt (2) but differs from the latter in the temperature gradient (T). Accordingly, the effective aluminium partitioning coefficient (k) determined in Experiment 7 does not satisfy the above-mentioned formula (1-1) also formula (1-2).

As a formula satisfying the effective aluminium partitioning coefficient (k) determined in the above-mentioned Experiment 1 to Experiment 3 and Experiment 4 to Experiment 6 and further satisfying the effective aluminium partitioning coefficient (k) determined in Experiment 7, obtained was the following formula (1-3):

$\begin{matrix} {k = {{\left\{ {{K_{1}^{\prime} \times {{Ln}(R)}} + K_{2}^{\prime}} \right\} \times \left\{ {K_{3}^{\prime} \times {\exp \left\lbrack {K_{4}^{\prime} \times R \times \left( {{K_{5}^{\prime} \times C_{2}} + K_{6}^{\prime}} \right)} \right\rbrack}} \right\} \times \left\{ {{K_{7}^{\prime} \times T} + K_{8}^{\prime}} \right\}} - K_{9}^{\prime}}} & \left( {1\text{-}3} \right) \end{matrix}$

[wherein k, R, C₂, K₁′, K₂′, K₃′, K₄′, K₅′ and K₆′ have the same meanings as above; and T means the temperature gradient (° C./mm)].

In formula (1-3), K₇′ is −0.4, K₈′ is 1.36, and K₉′ is 2.0×10⁻⁴.

The temperature gradient (T), the solidification speed (R), the aluminium concentration (C₂) in the starting silicon material melt (2) used and the effective aluminium partitioning coefficient (k) in Experiment 1 to Experiment 3, Experiment 4 to Experiment 6 and Experiment 7 satisfy the formula (1-3).

The data of K₁ to K₉ are determined according to the above formula (1) based on the above-mentioned data of K₁′ to K₉′ in the formula (1-3) established in the above, thereby giving the formula (1).

Example 1-1

The aluminium concentration (C₂) in the starting silicon material melt (2) is 1000 ppm; the predetermined maximum level of aluminium concentration (C_(10max)) is 4.0 ppm; the temperature gradient (T) is 0.9° C./mm; and the solidification speed (R) is 0.4 mm/min; and the standard solidification fraction (f₀) satisfying the formula (1) [wherein the values K₁ to K₉ are the same as those of K₁′ to K₉′, respectively] is determined, and is 0.18.

Using an apparatus of FIG. 1, a starting silicon material melt (2) having an aluminium concentration (C₂) of 1000 ppm was cooled in a mold (3) under a temperature gradient (T) (0.9° C./mm) condition so as to be solidified at a solidification speed (R) of 0.4 mm/min, thereby giving a directionally-solidified silicon (4) as shown in FIG. 2.

As in FIG. 2, the obtained directionally-solidified silicon (4) was cut at the part having a solidification fraction (f) in the cooling step of 0.18 to remove the region (45) that had been on the high-temperature side (22) under the temperature gradient (T), thereby giving a purified silicon (1). The maximum aluminium concentration (C_(1max)) of the purified silicon (1) was 4.0 ppm.

Example 1-2 and Example 2-1 to Example 7-2

A standard solidification fraction (f₀) was determined in the same manner as in Example 1-1 except that the aluminium concentration (C₂) of the starting silicon material melt (2), the predetermined maximum level of aluminium concentration (C_(10max)), the temperature gradient (T) and the solidification speed (R) were as in Table 4; then a directionally-solidified silicon (4) was produced also in the same manner as in Example 1-1 except that the temperature gradient (T) and the solidification speed (R) were as in Table 4; and the obtained directionally-solidified silicon (4) was cut at the part at which the solidification fraction (f) in the cooling step was the same as the standard solidification fraction (f₀), thereby giving a purified silicon (1). The maximum aluminium concentration (C_(1max)) of the purified silicon (1) is measured as shown in Table 4.

TABLE 4 C₂ C_(10max) T R C_(1max) Example No. ppm ppm f₀ ° C./mm mm/min ppm 1-1 1000 4.0 0.18 0.9 0.4 4.0 1-2 4.9 0.38 4.9 2-1 1000 2.8 0.17 0.9 0.2 2.8 2-2 4.2 0.38 4.2 3-1 1000 1.2 0.32 0.9 0.05 1.2 3-2 2.6 0.72 2.6 4-1 100 0.4 0.17 0.9 0.2 0.4 4-2 1.1 0.45 1.1 5-1 10 0.1 0.32 0.9 0.4 0.1 5-2 0.3 0.72 0.3 6-1 10 0.05 0.20 0.9 0.2 0.05 6-2 0.17 0.52 0.17 7-1 1000 3.1 0.17 0.4 0.2 3.1 7-2 6.7 0.52 6.7 

1. A process for producing a purified silicon by using a silicon melt as a starting material, comprising: a step of solidifying an aluminium-containing starting silicon material melt by cooling in a mold under a unidirectional temperature gradient (T (° C./mm)) condition to give a directionally-solidified silicon containing a purified silicon region having an aluminium concentration (C (ppm)) not higher than the predetermined maximum level of aluminium concentration (C_(10max) (ppm)) and a crude silicon region having an aluminium concentration (C) higher than the predetermined maximum level of aluminium concentration (C_(10max)), and a step of cutting off the crude silicon region from the obtained directionally-solidified silicon to give a purified silicon having an aluminium concentration (C) not higher than the predetermined maximum level of aluminium concentration (C_(10max)), wherein, in the step of cutting off the crude silicon region, the directionally-solidified silicon is cut at a part corresponding to a standard solidification fraction (f₀) obtained from the predetermined maximum level of aluminium concentration (C_(10max)) and the temperature gradient (T) and the solidification speed (R (mm/min)) in cooling the starting silicon material melt and satisfying the following formula (1) and formula (2), thereby cutting off the crude silicon region; the standard solidification fraction (f₀) indicates the ratio of the purified silicon region having an aluminium concentration (C (ppm)) not higher than the predetermined maximum level of aluminium concentration (C_(10max) (ppm)), to the whole of the directionally-solidified silicon, and 0≦f₀≦1; $\begin{matrix} {k = {{\left\{ {{K_{1} \times {{Ln}(R)}} + K_{2}} \right\} \times \left\{ {K_{3} \times {\exp \left\lbrack {K_{4} \times R \times \left( {{K_{5} \times C_{2}} + K_{6}} \right)} \right\rbrack}} \right\} \times \left\{ {{K_{7} \times T} + K_{8}} \right\}} - K_{9}}} & (1) \end{matrix}$ [in formula (1), k is a coefficient selected from a range of from 0.9 times to 1.1 times the effective aluminium partitioning coefficient k′, as obtained so as to satisfy the following formula (2): C _(10max) =k′×C ₂×(1−f ₀)^(k′−1)   (2), K₁ means a constant selected from a range of 1.1×10⁻³±0.1×10⁻³, K₂ means a constant selected from a range of 4.2×10⁻³±0.1×10⁻³, K₃ means a constant selected from a range of 1.2±0.1, K₄ means a constant selected from a range of 2.2±0.1, K₅ means a constant selected from a range of −1.0×10⁻³±0.1×10⁻³, K₆ means a constant selected from a range of 1.0±0.1, K₇ means a constant selected from a range of −0.4±0.1, K₈ means a constant selected from a range of 1.36±0.01, K₉ means a constant selected from a range of 2.0×10⁻⁴±1.0×10⁻⁴, R means a solidification speed (mm/min), T means a temperature gradient (° C./mm)], [in formula (2), C_(10max) means the predetermined maximum level of aluminium concentration (ppm) in purified silicon, C₂ means the aluminium concentration(ppm) in the starting silicon material melt, and f₀ means the standard solidification fraction].
 2. The process according to claim 1, wherein the predetermined maximum level of aluminium concentration (C_(10max)) is from 1/1000 times to 3/100 times the aluminium concentration (C₂) of the starting silicon material melt. 